"The Trump administration now seems to recognize it is in the best interest of U.S. corporations if the U.S. wins the trade conflict with a mild victory over China as opposed to crushing it into oblivion," wrote Nick Raich, CEO of The Earnings Scout, in a research note.

Overseas markets also rose amid hopes for progress in U.S.-China trade talks, while U.K. markets seemed to take in stride a "no confidence" vote in British Prime Minister Theresa May by her party's lawmakers scheduled for later today.

Conservative Party members have expressed frustrations with May over her negotiations of Britain's departure from the European Union, and many of them want a cleaner break from the trading bloc. Opposition lawmakers don't want Britain to leave the EU.

Investors also appear unfazed by President Donald Trump's threat to shut the government down unless Congress agrees to earmark $5 billion for funding construction of a border wall with Mexico.

"Although shutdowns get a lot of media hype, the reality is that stocks tend to take them in stride," LPL Senior Market Strategist Ryan Detrick said in a client note, adding that the S&P 500 has risen during each of the five previous government shutdowns.

Real progress, or optics?

China's top trade negotiator told U.S. officials that China would reduce tariffs on U.S. auto imports from 40 percent to 15 percent -- their level before the Trump administration imposed steeper tariffs on Chinese imports -- and agree to buy more soybeans and other crops from American farmers, according to the Wall Street Journal.

The discussions were also said to touch on some key trouble spots for the Trump administration, including what the U.S. says is Chinese pressure to force technology transfers from U.S. tech business to local partners.

Huawei CFO arrest stokes fears of trade war between China & U.S.

China also reportedly may modify its "Made in China 2025" plan, the country's goal of becoming the world's leader in robotics, artificial intelligence and other key technologies, to include language that would make it more open to non-Chinese companies, the Journal noted. Whether that will be enough to persuade the Trump administration that China has met its trade demands remains to be seen.

"Global markets are on the rise, as an improved U.S.-China trade outlook helps drive optimism," said Joshua Mahony, market analyst at IG. "The Chinese decision to cut tariffs on U.S. car imports is likely to be the beginning of a wider package of measures aimed at opening up trade pathways between the world's two largest economies."

Trade deficit still growing

Even as Mr. Trump pushes to narrow the trade deficit -- the difference between a country's exports and imports -- demand for foreign-made products is spurring companies to import more foreign-made goods to the U.S., pushing the trade gap to a 10-year high.

The tariffs levied on imports by the Trump administration added $2.8 billion in new costs for U.S. businesses in October, according to Tariffs Hurt the Heartland, a lobbying coalition of manufacturing, farming and technology groups.